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Simplifying -1x2 + 48x + -51 = 0 Reorder the terms: -51 + 48x + -1x2 = 0 Solving -51 + 48x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 51 + -48x + x2 = 0 Move the constant term to the right: Add '-51' to each side of the equation. 51 + -48x + -51 + x2 = 0 + -51 Reorder the terms: 51 + -51 + -48x + x2 = 0 + -51 Combine like terms: 51 + -51 = 0 0 + -48x + x2 = 0 + -51 -48x + x2 = 0 + -51 Combine like terms: 0 + -51 = -51 -48x + x2 = -51 The x term is -48x. Take half its coefficient (-24). Square it (576) and add it to both sides. Add '576' to each side of the equation. -48x + 576 + x2 = -51 + 576 Reorder the terms: 576 + -48x + x2 = -51 + 576 Combine like terms: -51 + 576 = 525 576 + -48x + x2 = 525 Factor a perfect square on the left side: (x + -24)(x + -24) = 525 Calculate the square root of the right side: 22.912878475 Break this problem into two subproblems by setting (x + -24) equal to 22.912878475 and -22.912878475.Subproblem 1
x + -24 = 22.912878475 Simplifying x + -24 = 22.912878475 Reorder the terms: -24 + x = 22.912878475 Solving -24 + x = 22.912878475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x = 22.912878475 + 24 Combine like terms: -24 + 24 = 0 0 + x = 22.912878475 + 24 x = 22.912878475 + 24 Combine like terms: 22.912878475 + 24 = 46.912878475 x = 46.912878475 Simplifying x = 46.912878475Subproblem 2
x + -24 = -22.912878475 Simplifying x + -24 = -22.912878475 Reorder the terms: -24 + x = -22.912878475 Solving -24 + x = -22.912878475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x = -22.912878475 + 24 Combine like terms: -24 + 24 = 0 0 + x = -22.912878475 + 24 x = -22.912878475 + 24 Combine like terms: -22.912878475 + 24 = 1.087121525 x = 1.087121525 Simplifying x = 1.087121525Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.912878475, 1.087121525}
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